FINANCE 12. Capital Structure and Cost of Capital Professor André Farber Solvay Business School Université Libre de Bruxelles Fall 2004

MBA 2004 Cost of capital |2 Risk and return and capital budgeting Objectives for this session: – Beta of a portfolio – Beta and leverage – Weighted average cost of capital – Modigliani Miller 1958

MBA 2004 Cost of capital |3 Beta of a portfolio Consider the following portfolio StockValueBeta An A  P A  A Bn B  P B  B The value of the portfolio is: V = n A  P A + n A  P B The fractions invested in each stock are: X i = ( n i P i ) / V for i = A,B The beta of the portfolio is the weighted average of the betas of the individual stocks  P = X A  A + X B  B

MBA 2004 Cost of capital |4 Example Stock$  X ATT3, Genetech2, V5,000  P = 0.60 * * 1.40 = 1.02

MBA 2004 Cost of capital |5 Application 1: cost of capital for a division Firm = collection of assets Example: A company has two divisions Value($ mio)  Electrical Chemical V600  firm = (100/600) * (0.50) + (500/600) * 0.90 = 0.83 Assume: r f = 5%r M - r f = 6% Expected return on stocks: r = 5% + 6%  0.83 = 9.98 % An adequate hurdle rate for capital budgeting decisions ? No The firm should use required rate of returns based on project risks: Electricity :  0.50 = 8% Chemical :  0.90 = 10.4%

MBA 2004 Cost of capital |6 Application 2: leverage and beta Consider an investor who borrows at the risk free rate to invest in the market portfolio Assets$  X Market portfolio2,00012 Risk-free rate-1, V1,000  P = 2  1 + (-1)  0 = 2

MBA 2004 Cost of capital |7 8% 14% 1 2 Beta M P 8% 14% 20% Sigma Expected Return M P

MBA 2004 Cost of capital |8 Cost of capital with debt Up to now, the analysis has proceeded based on the assumption that investment decisions are independent of financing decisions. Does the value of a company change the cost of capital change if leverage changes ?

MBA 2004 Cost of capital |9 An example CAPM holds – Risk-free rate = 5%, Market risk premium = 6% Consider an all-equity firm: Market value V100 Beta1 Cost of capital11% (=5% + 6% * 1) Now consider borrowing 10 to buy back shares. Why such a move? Debt is cheaper than equity Replacing equity with debt should reduce the average cost of financing What will be the final impact On the value of the company? (Equity + Debt)? On the weighted average cost of capital (WACC)?

MBA 2004 Cost of capital |10 Weighted Average Cost of Capital An average of: The cost of equity r equity The cost of debt r debt Weighted by their relative market values (E/V and D/V) Note: V = E + D

MBA 2004 Cost of capital |11 Modigliani Miller (1958) Assume perfect capital markets: not taxes, no transaction costs Proposition I: The market value of any firm is independent of its capital structure: V = E+D = V U Proposition II: The weighted average cost of capital is independent of its capital structure r wacc = r A r A is the cost of capital of an all equity firm

MBA 2004 Cost of capital |12 Using MM 58 Value of company: V = 100 InitialFinal Equity Debt 0 20 Total MM I WACC = r A 11%11% MM II Cost of debt-5% (assuming risk-free debt) D/V00.20 Cost of equity11%12.50% (to obtain r wacc = 11%) E/V100%80%

MBA 2004 Cost of capital |13 Why is r wacc unchanged? Consider someone owning a portfolio of all firm’s securities (debt and equity) with X equity = E/V (80% in example ) and X debt = D/V (20%) Expected return on portfolio = r equity * X equity + r debt * X debt This is equal to the WACC (see definition): r portoflio = r wacc But she/he would, in fact, own a fraction of the company. The expected return would be equal to the expected return of the unlevered (all equity) firm r portoflio = r A The weighted average cost of capital is thus equal to the cost of capital of an all equity firm r wacc = r A

MBA 2004 Cost of capital |14 What are MM I and MM II related? Assumption: perpetuities (to simplify the presentation) For a levered companies, earnings before interest and taxes will be split between interest payments and dividends payments EBIT = Int + Div Market value of equity: present value of future dividends discounted at the cost of equity E = Div / r equity Market value of debt: present value of future interest discounted at the cost of debt D = Int / r debt

MBA 2004 Cost of capital |15 Relationship between the value of company and WACC From the definition of the WACC: r wacc * V = r equity * E + r debt * D As r equity * E = Div and r debt * D = Int r wacc * V = EBIT V = EBIT / r wacc Market value of levered firm EBIT is independent of leverage If value of company varies with leverage, so does WACC in opposite direction

MBA 2004 Cost of capital |16 MM II: another presentation The equality r wacc = r A can be written as: Expected return on equity is an increasing function of leverage: rArA D/E r equity 11% r debt 5% % r wacc Additional cost due to leverage

MBA 2004 Cost of capital |17 Why does r equity increases with leverage? Because leverage increases the risk of equity. To see this, back to the portfolio with both debt and equity. Beta of portfolio:  portfolio =  equity * X equity +  debt * X debt But also:  portfolio =  Asset So: or

MBA 2004 Cost of capital |18 Back to example Assume debt is riskless: